Compare DNS, LES, and RANS approaches for turbulence simulation.

DNS (Direct Numerical Simulation) resolves all turbulent scales without modeling, requiring mesh size smaller than Kolmogorov scale (η = (ν³/ε)^(1/4)). Grid points scale as Re^(9/4), making it computationally prohibitive for industrial Re (>10⁶). Used for research and model validation. LES (Large Eddy Simulation) resolves large energy-containing eddies while modeling subgrid scales using SGS models (Smagorinsky, dynamic). Requires mesh resolving 80% of turbulent kinetic energy. 10-100x cheaper than DNS but still expensive. RANS averages all turbulence, solving time-averaged equations with turbulence models. 1000x cheaper than LES, suitable for industrial design. Hybrid DES/SAS methods combine RANS near walls with LES in separated regions.